# Computing immobilizing grasps of polygonal parts

## Abstract

The authors present the first algorithms for computing all placements of (frictionless) point fingers that put a polygonal part in form closure and all placements of point fingers that achieve second-order immobility of a polygonal part. The algorithms run in O(n{sup 2+{var_epsilon}}+K) and O(n{sup 2}log{sup 2}n+K) time in the case of form closure and second-order immobility, respectively, where n is the number of vertices of the polygon, K is the description size of the resulting set of finger placements, and {var_epsilon} is an arbitrarily small constant. The basic of the algorithm is a translation of the problem into geometric searching problems, which are solved using efficient data structures. The results can be extended to the problem of computing all placements of a line and two points that put a polygonal part in form closure. The resulting algorithm runs in O(n{sup 2}log{sup 2} n+K) time, where K is again the description size of the output.

- Authors:

- Publication Date:

- Research Org.:
- Utrecht Univ. (NL)

- OSTI Identifier:
- 20030407

- Alternate Identifier(s):
- OSTI ID: 20030407

- Resource Type:
- Journal Article

- Journal Name:
- International Journal of Robotics Research

- Additional Journal Information:
- Journal Volume: 19; Journal Issue: 5; Other Information: PBD: May 2000; Journal ID: ISSN 0278-3649

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION; ROBOTS; INDUSTRIAL PLANTS; ALGORITHMS; SHAPE; MOTION; MATERIALS HANDLING

### Citation Formats

```
Stappen, A.F. van der, Wentink, C., and Overmars, M.H.
```*Computing immobilizing grasps of polygonal parts*. United States: N. p., 2000.
Web. doi:10.1177/02783640022066978.

```
Stappen, A.F. van der, Wentink, C., & Overmars, M.H.
```*Computing immobilizing grasps of polygonal parts*. United States. doi:10.1177/02783640022066978.

```
Stappen, A.F. van der, Wentink, C., and Overmars, M.H. Mon .
"Computing immobilizing grasps of polygonal parts". United States. doi:10.1177/02783640022066978.
```

```
@article{osti_20030407,
```

title = {Computing immobilizing grasps of polygonal parts},

author = {Stappen, A.F. van der and Wentink, C. and Overmars, M.H.},

abstractNote = {The authors present the first algorithms for computing all placements of (frictionless) point fingers that put a polygonal part in form closure and all placements of point fingers that achieve second-order immobility of a polygonal part. The algorithms run in O(n{sup 2+{var_epsilon}}+K) and O(n{sup 2}log{sup 2}n+K) time in the case of form closure and second-order immobility, respectively, where n is the number of vertices of the polygon, K is the description size of the resulting set of finger placements, and {var_epsilon} is an arbitrarily small constant. The basic of the algorithm is a translation of the problem into geometric searching problems, which are solved using efficient data structures. The results can be extended to the problem of computing all placements of a line and two points that put a polygonal part in form closure. The resulting algorithm runs in O(n{sup 2}log{sup 2} n+K) time, where K is again the description size of the output.},

doi = {10.1177/02783640022066978},

journal = {International Journal of Robotics Research},

issn = {0278-3649},

number = 5,

volume = 19,

place = {United States},

year = {2000},

month = {5}

}